Related papers: Weak neural variational inference for solving Baye…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

This paper proposes a non-centered parameterization based infinite-dimensional mean-field variational inference (NCP-iMFVI) approach for solving the hierarchical Bayesian inverse problems. This method can generate available estimates from…

We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference…

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…

Solving general high-dimensional partial differential equations (PDE) is a long-standing challenge in numerical mathematics. In this paper, we propose a novel approach to solve high-dimensional linear and nonlinear PDEs defined on arbitrary…

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…

Solving inverse problems in scientific and engineering fields has long been intriguing and holds great potential for many applications, yet most techniques still struggle to address issues such as high dimensionality, nonlinearity and model…

Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…

Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the…

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…

Bayesian full waveform inversion (FWI) offers uncertainty-aware subsurface models; however, posterior sampling directly on observed seismic shot records is rarely practical at the field scale because each sample requires numerous…

In this study, an image-assisted Approximate Bayesian Computation (ABC) parameter inverse method is proposed to identify the design parameters. In the proposed method, the images are mapped to a low-dimensional latent space by Variational…

Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical…

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network (PI-VEGAN), that effectively tackles the forward, inverse, and mixed problems of stochastic…